Arora's PTAS uses quadtrees to attack a restrict case of this issue, which 
Arora's PTAS uses quadtrees to attack a restrict case of this issue, which is the target of the Christofides
 algorithm. A historical bound on it is given by the Held-Karp algorithm. If the triangle inequality holds,
 then the restricted case is known as metric; further constraints yield the Euclidean version of this problem.
 One solution to this problem is the "nearest neighbor" algorithm, though that solution is only optimal in
 certain cases. An early description of this problem included hypothetical routes through towns in Germany
 and Switzerland. For 10 points, name this optimization problem in computer science in which a merchant
 must determine the shortest path that will take him to each city in a route exactly once.
Arora's PTAS uses quadtrees to attack a restrict case of this issue, which is the target of the Christofides
 algorithm.
{traveling salesman} problem